Question

Assume IJK ~ PQR with medians IM and PN

to sides JK and QR respectively, IJ = 15, and
PQ = 9. If IM is 2 greater than PN, find both
medians.

Answer 1

Explanation:

Median IJK = IM = PN + 2

Median PQR = PN

Therefore, IM = PN + 2

IM = PN + 2

PN = IM - 2

IM = (15 + 9 + PN)/2

PN = (15 + 9 + IM - 2)/2

15 + 9 + PN = 2IM

15 + 9 + IM - 2 = 2PN

25 + PN = 2IM

25 + IM - 2 = 2PN

PN = 2IM - 25

PN = 2PN - 25

3PN = 25

PN = 25/3

IM = PN + 2

IM = 25/3 + 2

IM = 29/3

Therefore, IM = 29/3 and PN = 25/3.